Topic: The Cartesian Axis/Graphing Objective: I will be able to plot given points on an axis. How do I graph (x, y) coordinates on a Cartesian axis? Today’s Heading Space for YOUR questions during the lesson. This is for YOUR notes. You do NOT need to copy every word on the screen. Write what you need to. Things that may help: Vocab Examples Formulas

The Cartesian Axis

2.1 Linear Equations in Two Variables 1.The Rectangular Coordinate System Slide 3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The origin is the center of the axis, where the x and y axis meet. This is labeled as the ordered pair (0, 0). Origin = center of Cartesian axis

2.1 Linear Equations in Two Variables 1.The Rectangular Coordinate System Slide 4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Points graphed in a rectangular coordinate system are defined by two numbers as an ordered pair, (x, y). Ordered pair = (x, y)

2.1 Linear Equations in Two Variables 1.The Rectangular Coordinate System Slide 5 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The first number (called the x-coordinate) is the horizontal (left or right) position from the origin. x-coordinate = position left or right from the origin. Left = negative Right = Positive

2.1 Linear Equations in Two Variables 1.The Rectangular Coordinate System Slide 6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The second number (called the y-coordinate, or the ordinate) is the vertical position (up or down) from the origin. y-coordinate = position up or down from the origin Up = positive Down = Negative

1Plotting Points Slide 7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Plot each point and state the quadrant or axis where it is located.

Linear Equation in Two Variables Slide 9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Let A, B, and C be real numbers such that A and B are not both zero. Then, an equation that can be written in the form: Ax + By = C is called a linear equation in two variables. Solutions to linear equations are expressed as ordered pairs. Linear Equation = Ax + By = C

Linear Equation in Two Variables Slide 10 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solutions to linear equations are expressed as ordered pairs. To determine if an ordered pair is a solution to a linear equation, you can substitute, or plug in, the values given for each variable. Substitute = plug in numbers for variables

Example: x + 2y = 10 Show that (0, 5) is a solution. Linear Equation in Two Variables

2 Determining Solutions to a Linear Equation Slide 12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. For the linear equation –2x + 3y = 8, determine whether the ordered pair is a solution.